A look at motion in the frequency domain

A moving image can be specified by a contrast distribution, c(x,y,t), over the dimensions of space x,y, and time t. Alternatively, it can be specified by the distribution C(u,v,w) over spatial frequency u,v and temporal frequency w. The frequency representation of a moving image is shown to have a characteristic form. This permits two useful observations. The first is that the apparent smoothness of time-sampled moving images (apparent motion) can be explained by the filtering action of the human visual system. This leads to the following formula for the required update rate for time-sampled displays. W(c)=W(l)+ru(l) where w(c) is the required update rate in Hz, W(l) is the limit of human temporal resolution in Hz, r is the velocity of the moving image in degrees/sec, and u(l) is the limit of human spatial resolution in cycles/deg. The second observation is that it is possible to construct a linear sensor that responds to images moving in a particular direction. The sensor is derived and its properties are discussed

Uniform apparent contrast noise: A picture of the noise of the visual contrast detection system

A picture which is a sample of random contrast noise is generated. The noise amplitude spectrum in each region of the picture is inversely proportional to spatial frequency contrast sensitivity for that region, assuming the observer fixates the center of the picture and is the appropriate distance from it. In this case, the picture appears to have approximately the same contrast everywhere. To the extent that contrast detection thresholds are determined by visual system noise, this picture can be regarded as a picture of the noise of that system. There is evidence that, at different eccentricities, contrast sensitivity functions differ only by a magnification factor. The picture was generated by filtering a sample of white noise with a filter whose frequency response is inversely proportional to foveal contrast sensitivity. It was then stretched by a space-varying magnification function. The picture summmarizes a noise linear model of detection and discrimination of contrast signals by referring the model noise to the input picture domain

An orthogonal oriented quadrature hexagonal image pyramid

An image pyramid has been developed with basis functions that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The pyramid operates on a hexagonal sample lattice. The set of seven basis functions consist of three even high-pass kernels, three odd high-pass kernels, and one low-pass kernel. The three even kernels are identified when rotated by 60 or 120 deg, and likewise for the odd. The seven basis functions occupy a point and a hexagon of six nearest neighbors on a hexagonal sample lattice. At the lowest level of the pyramid, the input lattice is the image sample lattice. At each higher level, the input lattice is provided by the low-pass coefficients computed at the previous level. At each level, the output is subsampled in such a way as to yield a new hexagonal lattice with a spacing sq rt 7 larger than the previous level, so that the number of coefficients is reduced by a factor of 7 at each level. The relationship between this image code and the processing architecture of the primate visual cortex is discussed

The Effects of Blowing Over Various Trailing-edge Flaps on an NACA 0006 Airfoil Section, Comparisons with Various Types of Flaps on other Airfoil Sections, and an Analysis of Flow and Power Relationships for Blowing Systems

The results are presented of a two-dimensional investigation conducted to determine the effect of blowing over various types of trailing-edge flaps on a wing having the NACA 0006 airfoil section and a drooped-nose flap. The position and profile of the trailing-edge flap, the nozzle height, and the location of the flap with respect to the nozzle were found to be important variables. Data from many investigations were used to make an evaluation of the effects of blowing on lift. An analysis was made of flow and power relationships for blowing systems

Effect of Reynolds number on stability characteristics of a cruciform wing-body

An experimental investigation was conducted to determine the effect of Reynolds number on the stability characteristics of a body with cruciform wings at large angles of attack. Pressure distributions and force and moment data (axial force not measured) are presented for Mach 1.60 and 2.70, Reynolds numbers based on body diameter from approximately 130,000 to 2,800,000, and angles of attack from 0 deg to 50 deg. In general, the data show only small effects of Reynolds number throughout the range of test condition. Also discussed are force balance and pressure data that suggest a direct relationship between wind choking and the onset of a nonlinear stability variaton with angle of attack

The window of visibility: A psychological theory of fidelity in time-sampled visual motion displays

Many visual displays, such as movies and television, rely upon sampling in the time domain. The spatiotemporal frequency spectra for some simple moving images are derived and illustrations of how these spectra are altered by sampling in the time domain are provided. A simple model of the human perceiver which predicts the critical sample rate required to render sampled and continuous moving images indistinguishable is constructed. The rate is shown to depend upon the spatial and temporal acuity of the observer, and upon the velocity and spatial frequency content of the image. Several predictions of this model are tested and confirmed. The model is offered as an explanation of many of the phenomena known as apparent motion. Finally, the implications of the model for computer-generated imagery are discussed

The Spatial Standard Observer

The spatial standard observer is a computational model that provides a measure of the visibility of a target in a uniform background image or of the visual discriminability of two images. Standard observers have long been used in science and industry to quantify the discriminability of colors. Color standard observers address the spectral characteristics of visual stimuli, while the spatial standard observer (SSO), as its name indicates, addresses spatial characteristics. The SSO is based on a model of human vision. The SSO was developed in a process that included evaluation of a number of earlier mathematical models that address optical, physiological, and psychophysical aspects of spatial characteristics of human visual perception. Elements of the prior models are incorporated into the SSO, which is formulated as a compromise between accuracy and simplicity. The SSO operates on a digitized monochrome still image or on a pair of such images. The SSO consists of three submodels that operate sequentially on the input image(s): 1. A contrast model, which converts an input monochrome image to a luminance contrast image, wherein luminance values are expressed as excursions from, and normalized to, a mean; 2. A contrast-sensitivity-filter model that includes an oblique-effect filter (which accounts for the decline in contrast sensitivity at oblique viewing angles); and 3. A spatial summation model, in which responses are spatially pooled by raising each pixel to the power beta, adding the results, and raising the sum to the 1/b power. In this model, b=2.9 was found to be a suitable value. The net effect of the SSO is to compute a numerical measure of the perceptual strength of the single image, or of the visible difference (denoted the perceptual distance) between two images. The unit of a measure used in the SSO is the just noticeable difference (JND), which is a standard measure of perceptual discriminability. A target that is just visible has a measure of 1 JND

Does Group Size Matter? The Impact of Reciprocity on Giving in Local Faith Communities

We compare and contrast how group size affects the internal structure & relational dynamics of religious communities, ranging from small religious congregations to megachurches (in American society). Classic anthropological economic and evolutionary theory holds that reciprocity, particularly altruistic generalized reciprocity, is most likely to strongly influence small groups, especially kinship-based groups. In the case of non-kin groups, studies of behavior mimicking kin altruism have found that all forms of reciprocity, including extreme giving and high-cost behaviors, are most likely to be found in small social groups with tight bonds, particularly those with shared religious beliefs. In the case of larger groups and individuals who are less tightly bound, a different set of factors may be associated with giving and other forms of group interaction. Distribution and redistribution of resources through a mediator, leader or bureaucracy is often more typical of large-scale groups with less direct contact between giver and receiver. How does this dynamic apply to modern religious groups, such as megachurches? In this paper, we propose a conceptual framework for analyzing religious communities, ranging from small-scale and larger-scale churches. Based on theoretical concepts drawn from both Anthropology and Sociology, we indicate that as the social group size increases, the nature of giving, broadly defined, is altered, becoming less direct and less kin-like, and more outwardly focused. By contrast, smaller groups are more likely to focus on interior, direct, reciprocal giving and kin-like altruism on an ongoing basis. Because giving is important to individual happiness as well as to religious community identity, what lessons are there to be learned about best practices in how religious communities organize giving

A visual detection model for DCT coefficient quantization

The discrete cosine transform (DCT) is widely used in image compression and is part of the JPEG and MPEG compression standards. The degree of compression and the amount of distortion in the decompressed image are controlled by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. One approach is to set the quantization level for each coefficient so that the quantization error is near the threshold of visibility. Results from previous work are combined to form the current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color. A model-based method of optimizing the quantization matrix for an individual image was developed. The model described above provides visual thresholds for each DCT frequency. These thresholds are adjusted within each block for visual light adaptation and contrast masking. For given quantization matrix, the DCT quantization errors are scaled by the adjusted thresholds to yield perceptual errors. These errors are pooled nonlinearly over the image to yield total perceptual error. With this model one may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix